Understand Absolute Value of Rational Numbers
I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
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🎯 Content Objective / Objetivo de contenido
I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Why are -5 and 5 both the same distance from zero on the number line, even though one is negative and one is positive?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Beaker Temperatures
Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown. She needs to use the beaker with the temperature that is closer to 0°C. Which beaker should Claire use?
Concept Launch
💡 What is absolute value?
An integer is a whole number that can be positive, negative, or zero. The absolute value of a number is how far it is from zero on the number line. Distance is never negative.
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Your turn — fractions and decimals too
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Integers and Absolute Value Enteros y valor absoluto |
Integers are whole numbers and their opposites; absolute value is their distance from zero. Los enteros son números enteros y sus opuestos; el valor absoluto es su distancia desde cero. |
|−6| = 6 because −6 is 6 units from zero. | |
| Integer Número entero |
Whole numbers and their opposites, like -2, -1, 0, 1, 2. Un número entero que puede ser positivo, negativo o cero. |
... -3, -2, -1, 0, 1, 2, 3 ... shown on a number line with 0 in the center | |
| Positive Positivo |
A number bigger than zero, to the right of zero on a number line. Un número mayor que cero, a la derecha del cero en la recta numérica. |
+5 means 5 above zero, like 5 floors above ground level | |
| Negative Negativo |
A number smaller than zero, to the left of zero on a number line. Un número menor que cero, a la izquierda del cero en la recta numérica. |
-3 means 3 below zero, like 3 floors underground | |
| Absolute value Valor absoluto |
How far a number is from zero. It is never negative. Qué tan lejos está un número de cero. Nunca es negativo. |
|-5| = 5 and |5| = 5 — both are 5 units from 0 | |
| Opposite Opuesto |
Two numbers the same distance from zero, on opposite sides, like 3 and -3. Dos números a la misma distancia de cero, en lados opuestos, como 3 y -3. |
3 and -3 are opposites — both are 3 units from 0 |
Which Word Fits?
The distance of an integer from zero is its ___ ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Why are -5 and 5 both the same distance from zero on the number line, even though one is negative and one is positive?
👂 Listen For
Student says both are 5 units from zero (same absolute value) but are opposites because of their signs.
Extend: Push students to explain why absolute value can never be negative.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Plot each integer on the number line and find its absolute value (distance from zero).
✍️ Explore Discourse
How does the number line help you see the difference between an integer and its absolute value?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
A diver is at -30 feet and a hawk is at +30 feet. How can absolute value help you describe how far each is from sea level?
👂 Listen For
Student uses absolute value to show both are 30 feet from sea level (zero), ignoring direction.
Extend: Ask students to decide who is truly farther from sea level and justify using both the integers and their absolute values.
Practice Check A
Which statement about absolute value is TRUE?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which number has the LEAST absolute value: −1.5, 0.75, −1/4, or 2?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Expression Simplify
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Sort each label into the correct box.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign" — and it works because ___.
Because Integers and Absolute Value means ___, but a tricky part is ___, so I have to ___.
A common mistake with Integers and Absolute Value is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Integer to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign because ___
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign but ___
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each integer on the number line and find its absolute value (distance from zero).
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is the absolute value of -9?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A submarine is at -150 meters (below sea level) and a helicopter is at +200 meters (above sea level). A rescue team needs to know how far each is from sea level to plan a mission.
✍️ Connection Reasoning
How does absolute value help the rescue team compare the submarine and helicopter positions?
The submarine is at ___ meters, and its absolute value is ___ because ___. The helicopter is at ___ meters, and its absolute value is ___. Absolute value helps the rescue team because ___.
Turn & Talk — Connect
How is the opposite of a number different from the absolute value of a number?
👂 Listen For
Student explains the opposite flips the sign while absolute value always gives the non-negative distance from zero.
Extend: Push students to find a number whose opposite and absolute value are equal, and explain why.
Summarize: Understand Absolute Value of Rational Numbers
Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0). 1. Absolute value represents distance on a number line, never direction. 2. Distance is always positive or zero: |-7| = 7 and |7| = 7. 3. Context: Magnitude of temperature, debt, elevation regardless of sign
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which integer has an absolute value of 8 and is located to the LEFT of zero on the number line?
Bonus Exit Check
What is the absolute value of -9?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Student says both are 5 units from zero (same absolute value) but are opposites because of their signs.
• Student uses absolute value to show both are 30 feet from sea level (zero), ignoring direction.
• Student explains the opposite flips the sign while absolute value always gives the non-negative distance from zero.
• Student gives a real context (temperature, elevation, money) and explains zero as the reference point between positive and negative.
Common mistake: A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer. Absolute value measures distance from zero and is always positive or zero, but that distance does not decide which integer is greater — only left-to-right order on the number line does. Before you submit, ask: am I comparing distance from zero (absolute value) or position on the number line (greater/less than)?
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: |-4| = |4| because both are 4 units from zero — Absolute value measures distance from zero. Both -4 and 4 are 4 units from zero, so |-4| = |4| = 4.
✓ Practice 2: −1/4 — |−1/4| = 0.25, |0.75| = 0.75, |−1.5| = 1.5, |2| = 2. The number CLOSEST to zero — regardless of sign — is −1/4.
✓ Practice 3: 9 — Absolute value is the distance from zero. -9 is 9 units from zero, so |-9| = 9.
✓ Practice 4: 7 — |-3| = 3, |7| = 7, |-5| = 5, |2| = 2. The greatest absolute value is 7.
✓ Exit ticket: -8 — To the left of zero means negative. The integer -8 has an absolute value of 8 because it is 8 units from zero.